Question

Check my answers?

Answer 1

A box is to be formed by cutting square pieces out of the corner of a rectangular piece of a 4" by 6" note card as shown below. The sides will then be folded up to make a box.

Answer 2

Length = 6 - 2x
Width = 4 - 2x
Area = (6 - 2x)(4 - 2x)
^ that in standard form is 4x^2 - 20x + 24

Answer 3

Right so far?

Answer 4

You're correct

Answer 5

Okay. What I'm having trouble on is Part III of this problem.

Solve this equation and take note of any extraneous solutions. Explain why the answer is extraneous, and clearly state the correct answer.

Answer 6

I solved the equation to get (5 + (sqrt17))/2 and (5 - (sqrt 17))/2

What now?

Answer 7

Try solving the equation by factoring instead of using the quadratic equation.

Answer 8

..... You can't factor 4x^2 - 20x + 24

Answer 9

You can factor out a 4 from the whole equation; see what you can do from there.

Answer 10

Right, that's what I did before I solved using the quadratic formula.

Answer 11

I already solved the quadratic equation, I just don't know what to do from there.

Answer 12

Equate the quadratic to 16 and solve for x.

Answer 13

\[4(x^2-5x+6)\]
\[4(x-6)(x+1)\]

Answer 14

How did you get a +6 on the right side?

4x^2 - 20x + 8
Factor out 4 to get: x^2 - 5x + 2

Answer 15

@Kinged

Do you mean solve for x^2 - 5x + 2 = 16 ?

Answer 16

it's not +8, it's +24 (check your above comments)

Answer 17

Right... but the 16 is on the left side, so I subtracted 16 from 24 to get it into standard form. Was that step wrong?

Thanks for you help btw :)

Answer 18

I don't know why kinged said to set it equal to 16; set it equal to 0 (I might be wrong but idk where kinged got 16 from)

Answer 19

Yeah, set it = to 0

Answer 20

0 = x^2 - 5x + 2

Like that?

Answer 21

I plugged that into the quadratic formula to get \[(5 \pm \sqrt{17})/2\]

Answer 22

nono, just set your original standard form quadratic equation to 0

Answer 23

\[4x^2 -20x + 24=0\]

Answer 24

The formula for the Area is 4x^2 - 20x + 24 but the question is asking the equation if the area equals 16... so wouldn't I set it equal to 16 then? And solve for x?